We are given two tips for finding our graph, it has a max point and the point of the line is x = 3. Meaning that this graph must open down and should not go anything further than 3 on the y graph.

The only one that fits this proposition is the last graph. Making it correct.

8 0

2 years ago

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Write an equation in slope intercept form of the line passing through (8,1) and (1,8)

frosja888 [35]

Answer: y = -x + 9

Step-by-step explanation:

First, to find the slope of the line we will use: (y₂-y₁)/(x₂-x₁)

Using the two points, we get: (8-1)/(1-8)

Simplify it: 7/-7

Finally, the slope is -1

We can now write: y = -x + b

Next we will plug in a point into the equation we have:

(8,1) --> 1 = -8 + b Then solve algebraically

b = 9

Then finish the equation:

y = -x + 9

8 0

3 years ago

The length of a rectangle is 5 inches more than its width, x. The area of a rectangle can be represented by the equation x 2 + 5

Arada [10]

Answer:

Width = 15 inches Length = 20 inches

Step-by-step explanation:

The area of a rectangle is calculated using the following formula.

$A = Lx$ (1)

Where L is the length and x is the width of the rectangle

In this case we know that the length of the rectangle is 5 inches greater than its width. This means that:

$L = x + 5$ (2)

Also The area of a rectangle can be represented by the equation $x^2 + 5x = 300$

so to find the width x we solve the equation

$x^2 + 5x -300=0$ (3)

For an equation of the form $ax ^ 2 + bx + c = 0$ the quadratic formula is:

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$

In this case note that:

$a=1\\b=5\\c=-300$

Then:

$x=\frac{-5\±\sqrt{(5)^2-4(1)(-300)}}{2(1)}$

$x=\frac{-5\±\sqrt{25+1200}}{2}$

$x=\frac{-5\±\sqrt{1225}}{2}$

$x=\frac{-5\±35}{2}$

$x_1=\frac{-5+35}{2}$ → $x_1=15$

$x_2=\frac{-5-35}{2}$ → $x_2=-20$

We take the positive solution $x=15\ in$

Now we use equation (2) to find L

$L = x + 5$

$L = 15 + 5$

$L = 20\ in$

8 0

4 years ago

Sang-Jin has only quarters and nickels in her piggy bank. She has 66 coins in the bank with a value of $11.50.

asambeis [7]

Let x be quarters, and y be nickels.
0.25x + 0.05y = 11.50

x + y = 66

x= 66 - y

0.25(66-y)+0.05y=11.50
16.5 -0.25y+0.05y = 11.50
16.5-0.2y=11.50
-0.2y=11.50-16.5
-0.2y=-5
-0.2y/-0.22=-5/-0.2
y=25

x+y=66
x+(25)=66
x=66-25
x=41

So there are 41 quarters, and 25 nickels.

5 0

3 years ago